Question: Simplify the following expression: $q = \dfrac{x^2 - 10x + 21}{x - 7} $
First factor the polynomial in the numerator. $ x^2 - 10x + 21 = (x - 7)(x - 3) $ So we can rewrite the expression as: $q = \dfrac{(x - 7)(x - 3)}{x - 7} $ We can divide the numerator and denominator by $(x - 7)$ on condition that $x \neq 7$ Therefore $q = x - 3; x \neq 7$